Jean-Claude Carmona

L 1 - L 2 robust estimation in prediction error system identification

The problem of robust system identification with corrupted data remains a difficulty. In this paper we shall put ourselves in the prediction error framework. We shall present a mixed L1 -L2 estimator based on a parameterized objective function leading to an alternative solution fighting against the outliers, based on the well-known Hubers M-estimate. A simple physical insight on the main noise characteristics of the data leads to a convenient choice of the scaling factor which automatically determines the balance between L1 and L2 contributions in the estimation procedure. Moreover, a general formalism leads to concise expressions of the gradient and the Hessian of the objective function which facilitate the estimation algorithms synthesis. These expressions are established in the classical case of linear models. A new decision tool, namely the L1 — contribution function of the residuals is proposed, which helps the user to determine the convenient model. Finally, some results on the frequency response of the best estimate are given for a semi finite acoustic duct used as an experimental set-up.

On a Robust Modeling of Piezo-Systems

This paper proposes a new modeling approach which is experimentally validated on piezo-electric systems in order to provide a robust Black-box model for complex systems control. Industrial applications such as vibration control in machining and active suspension in transportation should be concerned by the results presented here. Generally one uses physical based approaches. These are interesting as long as the user cares about the nature of the system. However, sometimes complex phenomena occur in the system while there is not sufficient expertise to explain them. Therefore, we adopt identification methods to achieve the modeling task. Since the microdisplacements of the piezo-system sometimes generate corrupted data named observation outliers leading to large estimation errors, we propose a parameterized robust estimation criterion based on a mixed L2 – L1 norm with an extended range of a scaling factor to tackle efficiently these outliers. This choice is motivated by the high sensitivity of least-squares methods to the large estimation errors. Therefore, the role of the L1-norm is to make the L2-estimator more robust. Experimental results are presented and discussed. [DOI: 10.1115/1.4005499]

Mixed Estimators Variety for Model Order Reduction in Control Oriented System Identification

A new family of MLE type estimators for model order reduction in dynamical systems identification is presented in this paper. A family of distributions proposed in this work combines ( ) and ( ) distributions which are quantified by four parameters. The main purpose is to show that these parameters add degrees of freedom (DOF) in the estimation criterion and reduce the estimated model complexity. Convergence consistency properties of the estimator are analysed and the model order reduction is established. Experimental results are presented and discussed on a real vibration complex dynamical system and pseudo-linear models are considered.

Design methodology of a complex CKC mechanical joint with a representation energetic tool multi-Bond graph: application to the helicopter

Due to the operation of the rotor, the helicopter is subject to important vibration levels affecting namely the fatigue of the mechanical parts and the passenger comfort. Suspensions between the main gear box (MGB) and the fuselage help to filter theses problematic vibrations. Their design can be difficult since the filtering should be efficient for different types of external forces (pumping force and roll/pitch torque) which may appear during the flight. As passive solutions classically show their limits, intelligent active solutions are proposed so that the filtering can be adjusted according to the vibration sources. Such studies still suffer from a lack of tools and methods, firstly, necessary to the design of complex mechanical systems (due to their multi-phase multi-physics multi-interaction characteristic, ...) and secondly, to develop of an intelligent joint. The main objective of this chapter is to provide a methodology for designing and analyzing an intelligent joint using an energetic representation approach: the multibond graph (MBG). This method is applied here to a complex mechanical system with closed kinematic chains (CKC) which is the joint between the main gear box (MGB) and the aircraft structure of a helicopter. Firstly, the MBG method is analyzed. Secondly, after a brief state of art of the MGB-Fuselage joint, developments focus on the 2D and 3D modeling of the MGB-Fuselage joint with a MBG approach. The 20-sim software is used to conduct the simulation of bond graph. Finally, the MBG models results are presented, illustrating the potential of the MBG tool to predict the dynamic of a complex CKC mechanical system.

A new robust estimation approach: An extended threshold M-estimator procedure

In order to tackle more efficiently the parameters estimation of an Output Error (OE) models contaminated by outliers, we propose to extend the range of the scaling factor of a parameterized robust estimation criterion (PREC) in the Hubers M-estimates context based on a mixed norm. Moreover, since the gradient and the Hessian of the PREC present a nonlinear structure in the OE models, we propose a new method to establish an L-Finite Taylors Expansion of these expressions in order to provide the asymptotic covariance matrix of the robust estimator. We present the results of a Monte Carlo study and we compare some robust methods with respect to our procedure.

1/2 Nonlinear system identification: A balanced accuracy/complexity neural network approach

Even if nonlinear system identification tends to provide highly accurate models these last decades, the user still remains interested in finding the good balance between high accuracy models and moderate complexity. In this paper, both a dedicated neural network design and a model reduction approach are proposed in order to improve this balance. The proposed neural network design helps to reduce the number of parameters of the model after the training phase preserving the estimation accuracy of the non reduced model. Even if this reduction is achieved by a convenient choice of the activation functions and the initial conditions of the synaptic weights, it nevertheless leads to models among the most encountered in the literature assuring all the interest of such method. To validate the proposed approach, we identified the Wiener-Hammerstein benchmark nonlinear system proposed in SYSID2009 [1].

2/2 Training time optimization for balanced accuracy/complexity neural network models

Accuracy, complexity and computational cost are very important characteristics of a model. In this paper, a dedicated neural network design and a computational cost reduction approach are proposed in order to improve the balance between the quality and computational cost of black box non linear system identification models. The proposed architecture helps to reduce the number of parameters of the model after the training phase preserving the estimation accuracy of the non reduced model. Here, we focus on the fact that this particular design helps to reduce the computational cost required for the training phase. To validate the proposed approach, we identified the Wiener-Hammerstein benchmark nonlinear system proposed in SYSID2009 [1].

Bond Graph Modeling and Simulation of a Vibration Absorber System in Helicopters

In the last 20 years, computer science has considerably progressed and there has been a resurgence of interest in bond graphs. The evolution of bond graph software has allowed for the full exploitation of its graphical aspects and for its simulation directly from the modeling environment without the need for the modeler to derive the associated dynamic equations. However, within this last decade, few simulations of complex multibody systems modeled with bond graphs have been conducted directly from a graphic software platform.

Design Methodology of a Complex CKC Mechanical Joint with an Energetic Representation Tool “Multibond Graph”: Application to the Helicopter

Due to the operation of the rotor, the helicopter is subject to important vibration levels affecting namely the fatigue of the mechanical parts and the passenger comfort. Suspensions between the main gear box (MGB) and the fuselage help to filter theses problematic vibrations. Their design can be difficult since the filtering should be efficient for different types of external forces (pumping force and roll/pitch torque) which may appear during the flight. As passive solutions classically show their limits, intelligent active solutions are proposed so that the filtering can be adjusted according to the vibration sources. Such studies still suffer from a lack of tools and methods, firstly, necessary to the design of complex mechanical systems (due to their multi-phase multi-physics multi-interaction characteristic, ...) and secondly, to develop of an intelligent joint. The main objective of this chapter is to provide a methodology for designing and analyzing an intelligent joint using an energetic representation approach: the multibond graph (MBG). This method is applied here to a complex mechanical system with closed kinematic chains (CKC) which is the joint between the main gear box (MGB) and the aircraft structure of a helicopter. Firstly, the MBG method is analyzed. Secondly, after a brief state of art of the MGB-Fuselage joint, developments focus on the 2D and 3D modeling of the MGB-Fuselage joint with a MBG approach. The 20-sim software is used to conduct the simulation of bond graph. Finally, the MBG models results are presented, illustrating the potential of the MBG tool to predict the dynamic of a complex CKC mechanical system.

Robust modeling of piezoelectric actuators for vibration drilling control

We present in this paper a new modeling approach on piezoelectric systems to get black-box pseudolinear models for the vibration drilling control. In these systems, complex phenomena occur, due to atypical changes of the process behavior, output noise or some hard non-linearities. Accordingly, identification methods to achieve the modeling task is preferred. The microdisplacements of the piezoelectric systems generate outliers in the output data, involving large errors in the estimated residuals. To deal efficiently with these data, a robust estimator is adopted. From the Hubers p-norm in which the tuning constant is extended, we propose a parameterized robust estimation criterion (PREC) and we get the asymptotic covariance matrix of the M-estimator for the Output Error model structure. A new decisional tool for the models validation, named L1-contribution function is proposed. Experimental results are presented and discussed.